Lesson 5

The purpose of this How Many Do You See is for students to use grouping strategies to describe the images they see. In the synthesis, students describe how they saw the dots and whether the groups of dots have an even or odd number of members. When recording responses, include equations with equal addends to help students make the connection to even numbers being written as the sum of two equal addends and odd numbers being written as 2 equal addends +1.

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash image.
• 30 seconds: quiet think time

• Display image.
• 1 minute: partner discussion
• Record responses with equations.
• Repeat for each image.

• “¿Cuáles imágenes muestran grupos pares de puntos?” // “Which images show even groups of dots?” (image 1 and image 3)
• “¿Cómo pueden saberlo usando las ecuaciones que anotamos?” // “How can you tell using the equations we recorded?”

The purpose of this activity is for students to describe patterns in the sequence of even and odd numbers when they count by 1. Students notice that even numbers are numbers that you count when you skip-count by 2 (MP7).

In order for all students to visualize the sequence, perform the activity where the whole class can be arranged in a circle with space for students to sit and stand. Depending on class size, the count may go beyond 20. It is ok for students to notice and wonder about even and odd numbers beyond 20, but maintain the focus throughout the lesson on numbers within 20.

• Form the class into a circle with all students standing.
• “Vamos a contar juntos de 1 en 1. La primera persona que cuenta dice 0 y se queda de pie” // “We are going to count together by 1. The first person to count will say 0 and stay standing.”
• “La siguiente persona dice su número y se sienta. La siguiente persona dice su número y se queda de pie” // “The next person will say their number and sit down. The next person will say their number and stay standing.”
• “Vamos a seguir contando hasta que todos hayan dicho un número” // “We will keep counting until everyone has said a number.”
• As needed, demonstrate the stand-sit-stand-sit sequence.
• Record the count:

  

  

• Prompt students who are standing to say their numbers. (0, 2, 4, …)
• Prompt students who are sitting to say their numbers. (1, 3, 5, …)

• “Escriban lo que observan y lo que se preguntan sobre los números de nuestro conteo” // “Write down what you notice and what you wonder about the numbers in our count.”
• 3 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students' responses that focus on even and odd number patterns to share in synthesis.

• Share and record student responses.
• Display:

  

  

• “Estas son las listas de todos los números pares y todos los números impares del 0 al 20” // “This is a list of all the even and odd numbers from 0 to 20.”
• “¿Qué patrones observan?” // “What patterns do you notice?” (All the even numbers are numbers you say when you skip-count by 2. The digits 0, 2, 4, 6, 8 repeat in the ones place for even numbers. The digits 1, 3, 5, 7, 9 repeat in the ones place in odd numbers.)
• “¿Cómo pueden usar estos patrones para saber si un número de objetos es par o es impar?” // “How could you use these patterns to tell if a number of objects is even or odd?” (If the number is an even number you say it when you skip-count by 2.)

The purpose of this activity is for students to make and test conjectures about the effect of adding 1 and adding 2 on the parity of a group of objects. They use what they know about equal groups, pairs, and skip-counting to explain why adding 1 may change whether a group of objects is even or odd and why adding 2 will have no effect (MP3, MP8).

• Groups of 2
• Give students recording sheets and access to counters.
• Draw:

  

  

• “Si agregamos 1 círculo más a este grupo, ¿esto cambiará el hecho de que el grupo tenga un número par o impar de círculos?” // “If we add 1 more circle to this group, will it change if the group has an even or odd number?” (Yes. It’s odd, so if you add 1 circle you’d make another pair and it’d be even.)
• 30 seconds: quiet think time
• Share responses.
• “¿Agregar 1 siempre cambia el hecho de que el número de objetos sea par o sea impar?” // “Does adding 1 always change whether a number of objects is even or odd?” (Yes. If you add 1 to an odd number, you’d always make a new pair, and the sum would be even. If it’s even, and you add 1, you’d have a leftover, so the sum would be odd. No. I think it works with some numbers, but maybe not all numbers.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “Pongamos a prueba nuestras ideas. Completen las dos primeras columnas de la tabla. Si tienen tiempo, prueben con otros números” // “Let’s test our ideas. Complete the first two columns of the table. You can test other numbers if you have time.”
• 4 minutes: independent work time
• 2 minutes: partner discussion
• “Si le sumamos 2 más a un grupo, ¿esto cambiará el hecho de que el grupo tenga un número par o tenga un número impar de objetos?” // “If we add 2 more to a group, will it change if the group has an even or odd number?” (No. For even, it’d be like counting by 2, the next number is even too. When we counted on 2 to odd, we made a list of odd numbers. Yes. I think if you add to a number, it’s going to change some numbers.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• “Pongamos a prueba lo que pensamos. Completemos la columna "agrega 2 fichas" de la tabla. Si les queda tiempo, pueden probar con otros números” // “Let’s test our thinking. Complete the table for the “add 2 counters” column. You can test other numbers if you have time.”
• 4 minutes: independent work time
• 2 minutes: partner discussion

• Display student conjectures from launch.
• “Usemos las fichas de Jada para mostrar cuáles de nuestras ideas son verdaderas” // “Let’s use Jada’s counters to show which of our ideas are true.”
• Invite students to share how they filled in the row about Jada's counters. 
• Display:

  • \(16 = 8 + 8\)

    \(17 = 8 + 8 + 1\)

    \(18 = 8 + 8 + 2\)

• “¿Cómo muestran estas ecuaciones que sumarle 1 a un número cambia el hecho de que el número sea par o impar, pero que sumarle 2 no lo cambia?” // “How do these equations show that adding 1 changes whether a number is even or odd, but adding 2 does not?” (You can see 2 equal groups of 8 in each. 17 is odd because there is one left out. 18 is even because you have 2 equal groups and 1 pair. You could give each group 1 to make it \(18 = 9 + 9\).)